Causal models are crucial for understanding complex systems and identifying causal relationships among variables. Even though causal models are extremely popular, conditional probability calculation of formulas involving interventions pose significant challenges. In case of Causal Bayesian Networks (CBNs), Pearl assumes autonomy of mechanisms that determine interventions to calculate a range of probabilities. We show that by making simple yet often realistic independence assumptions, it is possible to uniquely estimate the probability of an interventional formula (including the well-studied notions of probability of sufficiency and necessity). We discuss when these assumptions are appropriate. Importantly, in many cases of interest, when the assumptions are appropriate, these probability estimates can be evaluated using observational data, which carries immense significance in scenarios where conducting experiments is impractical or unfeasible.

Our focus in this paper is to solve causal inference problems using only observational data and (potentially partial) knowledge on the causal graph of the underlying structural causal model (SCM).

In this section, we provide proof for the disentanglement identifiability of the inferred exogenous variable. Our proof consists of three main components. Then we have ( f, T, λ) ( f, T, λ) . The conditional V AE, in this case, inherits all the properties of maximum likelihood estimation. The following proof is based on the reduction to absurdity.

Often, however, the causal relationship may be entirely absent or account only for a part of the initially observed correlation.

Constructing a directed cyclic graph (DCG) is challenged by both algorithmic difficulty and computational burden. Comparing multiple DCGs is even more difficult, compounded by the need to identify dynamic causalities across graphs.